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| In [[mathematics]], the '''Minkowski–Hlawka theorem''' is a result on the [[lattice packing]] of [[hypersphere]]s in dimension ''n'' > 1. It states that there is a [[lattice (group)|lattice]] in [[Euclidean space]] of dimension ''n'', such that the corresponding best packing of hyperspheres with centres at the [[lattice point]]s has density Δ satisfying
| | The title of the writer is Numbers. To gather coins is a thing that I'm totally addicted to. Her family life in Minnesota. Since she was eighteen she's been working as a receptionist but her promotion by no means comes.<br><br>Feel free to visit my web blog: home std test ([http://www.siccus.net/blog/15356 straight from the source]) |
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| :<math>\Delta \geq \frac{\zeta(n)}{2^{n-1}},</math>
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| with ζ the [[Riemann zeta function]]. Here as ''n'' → ∞, ζ(''n'') → 1. The proof of this theorem is nonconstructive, however, and it is still not known how to construct lattices with packing densities exceeding this bound for arbitrary ''n''.
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| This is a result of [[Hermann Minkowski]] (1905, not published) and [[Edmund Hlawka]] (1944). The result is related to a linear lower bound for the [[Hermite constant]].
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| ==See also==
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| *[[Kepler conjecture]]
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| ==References==
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| *{{cite book
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| | first = John H.
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| | last = Conway
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| | authorlink = John Horton Conway
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| | coauthors = [[Neil Sloane|Neil J.A. Sloane]]
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| | year = 1999
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| | title = Sphere Packings, Lattices and Groups
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| | edition = 3rd ed.
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| | publisher = Springer-Verlag
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| | location = New York
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| | isbn = 0-387-98585-9
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| }}
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| {{DEFAULTSORT:Minkowski-Hlawka theorem}}
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| [[Category:Geometry of numbers]]
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| [[Category:Theorems in geometry]]
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Latest revision as of 01:50, 30 December 2014
The title of the writer is Numbers. To gather coins is a thing that I'm totally addicted to. Her family life in Minnesota. Since she was eighteen she's been working as a receptionist but her promotion by no means comes.
Feel free to visit my web blog: home std test (straight from the source)